Prehistoric ceramic containers were tools used in culinary and ceremonial activity. The archaeological record preserves fragmentary remains of these ceramic tools, challenging the archaeologist to interpret their use and function from potsherds rather than from whole pots. We introduce the two-curvature method for reconstructing ceramic vessel shape and volume from assemblages of potsherds. Each point on a ceramic vessel or sherd has two dimensions of curvature, profile and axial. Profile curvature is sensitive to vessel shape, and axial curvature is sensitive to vessel diameter. Since vessel curvature and sherd curvature are the same, measuring profile and axial curvatures of potsherds provides information on parent-vessel shape and size. The two-curvature method is tested with replicated vessels, and its accuracy for measuring vessel parameters from sherd curvatures is assessed. Vessel parameters are estimated accurately from average-sherd-curvature measurements. Data gathered by using this method, on an archaeological assemblage of Kumeyaay ceramics from southern California, show that Kumeyaay pottery consists of 85–90 percent open-mouth hemispherical bowls and 10–15 percent closed-mouth spherical ollas. Through time, Kumeyaay vessel volume increased while vessel shape remained consistent.